2018/08/16 by Andrzej Olbryś, Olbryś, Andrzej
Mathematics · #26A51 #26B25 #26D15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1808.06524
openalex publication_date 2018/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper we solve a problem posed by Tomasz Szostok who asked about the solutions f and F to the system of inequalities f((x+y)/(2))≤ (F(y)-F(x))/(y-x)≤ (f(x)+f(y))/(2). We show that f and F are the solutions to the above system of inequalities if and only if f is a continuous convex function and F is primitive function of f. This result can be interpreted as a regularity phenomenon-the solutions to the system of functional inequalities turn out to be regular without any additional assumptions.